Conundrum – impossible mix of ingredients

I am amazed by the knowledge possessed by and shared on this forum! With all of that amassed info, however, I am still stymied. My 4.5 yr old chessie/lab mix just pronounced with food allergies over the last few months. He was eating Blue Buffalo until they changed the formula. His vet tests revealed he can tolerate wheat, chicken, beef, potatoes, and corn with no problem, but cannot tollerate rice, salmon, duck, turkey, lamb, or oats. That limits his protein sources and is a very hard combo to find- nearly all have some oats, fish or turkey. After recent info about grains being important to a dogs diet, I was searching for any brand that combined chix with wheat, but without any of the other offensive ingredients. I haven’t found one yet! I appreciated the food wizard provided by a poster, and it helped me narrow the list down to 3 possibilities. But all 3 have something in it that he can’t have, so I will have to see what he is least reactive to thru trial and error. Absent cooking his meals, can you offer any advice? If I do end up cooking for him, will I need to add supplements to insure he gets all the vitamins, minerals, oils, etc. he needs?

Ann Bixbi is very limited ingredients . This is Bixbi Beef ingredients
Beef, Beef Liver, Beef Kidney, Beef Bone, Pumpkin, Coconut Oil, Salmon Oil, Selenium Yeast, Vitamin E Supplement, Manganese Proteinate, Riboflavin Supplement, Calcium Iodate, d-Calcium Pantothenate, Mixed Tocopherols (a preservative), Rosemary Extract.
I feed their Rawbble freeze dried as toppers. Very pure food.
Dog Food Advisor rates their freeze dried a 5*. Hoping he does a review for 2019 of their kibble also.
Also: Diets in cases reported to the FDA frequently list potatoes or multiple legumes such as peas, lentils, other “pulses” (seeds of legumes), and their protein, starch and fiber derivatives early in the ingredient list, indicating that they are main ingredients. Early reports from the veterinary cardiology community indicate that the dogs consistently ate these foods as their primary source of nutrition for time periods ranging from months to years. https://www.fda.gov/AnimalVeterinary/NewsEvents/CVMUpdates/ucm613305.htm

Please keep in mind that there is no accurate way to test for food allergies. While tests exist, dogs will test positive to foods they have no allergic reactions to and can test negative to the foods that they react to.

For information on food allergies and how to diagnose and treat them go to veterinarypartner(dot) com and search on food allergy

The only way to diagnose food allergy is through an elimination food trial. A food specifically made for this purpose can be acquired through your veterinarian. Home cooking is also an option.

Limited ingredient diets often contain protein sources not listed in the ingredients and are not suitable to use as a test diet.
Best of Luck!